cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A134510 A112552 * A128174.

Original entry on oeis.org

1, 1, 1, 3, 1, 1, 4, 4, 1, 1, 8, 5, 5, 1, 1, 12, 12, 6, 6, 1, 1, 21, 17, 17, 7, 7, 1, 1, 33, 33, 23, 23, 8, 8, 1, 1, 55, 50, 50, 30, 30, 9, 9, 1, 1, 88, 88, 73, 73, 38, 38, 10, 10, 1, 1
Offset: 1

Views

Author

Gary W. Adamson, Oct 28 2007

Keywords

Comments

Row sums = the nonzero terms of A001629: (1, 2, 5, 10, 20, 38, 71, ...) such that A001629(n+1) = row sums of triangle A134510.

Examples

			First few rows of the triangle:
   1;
   1,  1;
   3,  1,  1;
   4,  4,  1,  1;
   8,  5,  5,  1,  1;
  12, 12,  6,  6,  1,  1;
  21, 17, 17,  7,  7,  1,  1;
  33, 33, 23, 23,  8,  8,  1,  1;
  55, 50, 50, 30, 30,  9,  9,  1,  1;
  ...

Crossrefs

Cf. A112552, A128174, A001629.

Formula

A112552 * A128174 as infinite lower triangular matrices.

A135151 A002260 + A128174 - I, I = Identity matrix.

Original entry on oeis.org

1, 1, 2, 2, 2, 3, 1, 3, 3, 4, 2, 2, 4, 4, 5, 1, 3, 3, 5, 5, 6, 2, 2, 4, 4, 6, 6, 7, 1, 3, 3, 5, 5, 7, 7, 8, 2, 2, 4, 4, 6, 6, 8, 8, 9, 1, 3, 3, 5, 5, 7, 7, 9, 9, 10
Offset: 1

Views

Author

Gary W. Adamson, Nov 21 2007

Keywords

Comments

A135152 is a companion triangle, both having row sums = A047838: (1, 3, 7, 11, 17, 23, 31, 39, ...).

Examples

			First few rows of the triangle:
  1;
  1, 2;
  2, 2, 3;
  1, 3, 3, 4;
  2, 2, 4, 4, 5;
  1, 3, 3, 5, 5, 6;
  2, 2, 4, 4, 6, 6, 7;
  ...

Crossrefs

Cf. A002260, A047838, A135152.

Formula

A002260 + A128174 - I, where I = Identity matrix, A002260 = (1; 1,2; 1,2,3; ...) and A128174 = (1; 0,1; 1,0,1; 0,1,0,1; ...).

A135152 A004736 + A128174 - I, I = Identity matrix.

Original entry on oeis.org

1, 2, 1, 4, 2, 1, 4, 4, 2, 1, 6, 4, 4, 2, 1, 6, 6, 4, 4, 2, 1, 8, 6, 6, 4, 4, 2, 1, 8, 8, 6, 6, 4, 4, 2, 1, 10, 8, 8, 6, 6, 4, 4, 2, 1, 10, 10, 8, 8, 6, 6, 4, 4, 2, 1
Offset: 1

Views

Author

Gary W. Adamson, Nov 21 2007

Keywords

Comments

Row sums = A047838: (1, 3, 7, 11, 17, 23, 31, 39, ...). The triangle is a companion to A135151.

Examples

			First few rows of the triangle:
  1;
  2, 1;
  4, 2, 1;
  4, 4, 2, 1;
  6, 4, 4, 2, 1;
  6, 6, 4, 4, 2, 1;
  8, 6, 6, 4, 4, 2, 1;
  ...

Crossrefs

Cf. A135151, A047838, A004736, A128174.

Formula

A004736 + A128174 - I, where I = Identity matrix, A004736 = (1; 2,1; 3,2,1; ...) and A128174 = (1; 0,1; 1,0,1; 0,1,0,1; ...).

A128189 Moebius transform of A128174.

Original entry on oeis.org

1, -1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, -1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, -1, 1, -1, 1, 0, 1, 0, 1
Offset: 1

Views

Author

Gary W. Adamson, Feb 17 2007

Keywords

Comments

Row sums = A083290: (1, 0, 1, 1, 2, 1, 3, 2, 3, 2, ...).

Examples

			First few rows of the triangle:
   1;
  -1, 1;
   0, 0, 1;
   0, 0, 0, 1;
   0, 0, 1, 0, 1;
  ...

Crossrefs

Cf. A051731, A128174, A083290.

Formula

A054525 * A128174 as infinite lower triangular matrices.

A128521 A128174 * A054525 * A000012.

Original entry on oeis.org

1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 2, 2, 1, 1, 0, 0, 1, 2, 1, 1, 1, 3, 3, 2, 2, 1, 1, 0, 0, 1, 2, 2, 2, 1, 1, 1, 3, 3, 3, 3, 2, 2, 1, 1, 0, -1, 1, 2, 2, 3, 2, 2, 1, 1
Offset: 1

Views

Author

Gary W. Adamson, Mar 07 2007

Keywords

Comments

Row sums = A106477: (1, 1, 3, 3, 7, 5, 13, 9, 19, 13, ...). A128522 = A054525 * A128174 * A000012.

Examples

			First few rows of the triangle:
  1;
  0, 1;
  1, 1, 1;
  0, 1, 1, 1;
  1, 2, 2, 1, 1;
  0, 0, 1, 2, 1, 1;
  1, 3, 3, 2, 2, 1, 1;
  0, 0, 1, 2, 2, 2, 1, 1;
  ...

Crossrefs

Cf. A128174, A054525, A000012, A106477, A128522.

Formula

A128174 * A054525 * A000012 as infinite lower triangular matrices.

A128522 A054525 * A128174 * A000012.

Original entry on oeis.org

1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 3, 3, 3, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 3, 3, 3, 3, 3, 2, 2, 1, 1, 2, 2, 2, 3, 2, 3, 2, 2, 1, 1
Offset: 1

Views

Author

Gary W. Adamson, Mar 07 2007

Keywords

Comments

Row sums = A123323: (1, 1, 3, 4, 8,7, 15, 14, ...). Left column = A083290: (1, 0, 1, 1, 2, 1, 3, 2, 3, 2, ...) A128521 = A128174 * A054525 * A000012.

Examples

			First few rows of the triangle:
  1;
  0, 1;
  1, 1, 1;
  1, 1, 1, 1;
  2, 2, 2, 1, 1;
  1, 1, 1, 2, 1, 1;
  3, 3, 3, 2, 2, 1, 1;
  2, 2, 2, 2, 2, 2, 1, 1;
  3, 3, 3, 3, 3, 2, 2, 1, 1;
  ...

Crossrefs

Cf. A054525, A128174, A000012, A083290, A123323, A128521.

Formula

A054525 * A128174 * A000012 as infinite lower triangular matrices.

A130266 A051340 * A128174.

Original entry on oeis.org

1, 1, 2, 4, 1, 3, 2, 5, 1, 4, 7, 2, 6, 1, 5, 3, 8, 2, 7, 1, 6, 10, 3, 9, 2, 8, 1, 7, 4, 11, 3, 10, 2, 9, 1, 8, 13, 4, 12, 3, 11, 2, 10, 1, 9, 5, 14, 4, 13, 3, 12, 2, 11, 1, 10, 16, 5, 15, 4, 14, 3, 13, 2, 12, 1, 11, 6, 17, 5, 16, 4, 15, 3, 14, 2, 13
Offset: 0

Views

Author

Gary W. Adamson, May 18 2007

Keywords

Comments

Row sums = A014255: (1, 3, 8, 12, 21, 27, 40, ...).
Left border = A123684: (1, 1, 4, 2, 7, 3, 10, 4, ...).

Examples

			First few rows of the triangle:
   1;
   1, 2;
   4, 1, 3;
   2, 5, 1, 4;
   7, 2, 6, 1, 5;
   3, 8, 2, 7, 1, 6;
  10, 3, 9, 2, 8, 1, 7;
  ...

Crossrefs

Cf. A051340, A128174, A014255, A123684.

Programs

  • Maple
    A128174 := proc(n,k)
    if k > n or k < 1 then
        0;
    else
        modp(k+n+1,2) ;
    end if;
end proc:
A051340 := proc(n,k)
    if k = n then
        n ;
    elif k <= n then
        1;
    else
        0;
    end if;
end proc:
A130266 := proc(n,k)
    add( A051340(n,j)*A128174(j,k),j=k..n) ;
end proc:
seq(seq(A130266(n,k),k=1..n),n=1..15) ; # R. J. Mathar, Aug 06 2016

Formula

A051340 * A128174 as infinite lower triangular matrices.

A131227 2*A051340 - A128174.

Original entry on oeis.org

1, 2, 3, 1, 2, 5, 2, 1, 2, 7, 1, 2, 1, 2, 9, 2, 1, 2, 1, 2, 11, 1, 2, 1, 2, 1, 2, 13, 2, 1, 2, 1, 2, 1, 2, 15, 1, 2, 1, 2, 1, 2, 1, 2, 17, 2, 1, 2, 1, 2, 1, 2, 1, 2, 19
Offset: 0

Views

Author

Gary W. Adamson, Jun 20 2007

Keywords

Comments

Row sums = A047383, numbers congruent to {1,5} mod 7: (1, 5, 8, 12, 15, 19, ...)

Examples

			First few rows of the triangle:
  1;
  2, 3;
  1, 2, 5;
  2, 1, 2, 7;
  1, 2, 1, 2, 9;
  2, 1, 2, 1, 2, 11;
  1, 2, 1, 2, 1,  2, 13;
  ...

Crossrefs

Cf. A051340, A128174, A047383, A131228, A131229.

Formula

2*A051340 - A128174 as infinite lower triangular matrices.

A131231 3*A130296 - 2*A128174.

Original entry on oeis.org

1, 6, 1, 7, 3, 1, 12, 1, 3, 1, 13, 3, 1, 3, 1, 18, 1, 3, 1, 3, 1, 19, 3, 1, 3, 1, 3, 1, 24, 1, 3, 1, 3, 1, 3, 1, 25, 3, 1, 3, 1, 3, 1, 3, 1
Offset: 1

Views

Author

Gary W. Adamson, Jun 20 2007

Keywords

Comments

Left column = A047225, numbers congruent to {0,1} mod 6: (1, 6, 7, 12, 13, 18, 19, ...).
Row sums = A131229, numbers congruent to {1,7} mod 10: (1, 7, 11, 17, ...).

Examples

			First few rows of the triangle:
   1;
   6, 1;
   7, 3, 1;
  12, 1, 3, 1;
  13, 3, 1, 3, 1;
  ...

Crossrefs

Cf. A131229, A047225, A130296, A128174.

Formula

3*A130296 - 2*A128174 as infinite lower triangular matrices.

A131911 2*A131821 - A128174.

Original entry on oeis.org

1, 4, 3, 5, 2, 5, 8, 1, 2, 7, 9, 2, 1, 2, 9, 12, 1, 2, 1, 2, 11, 13, 2, 1, 2, 1, 2, 13, 16, 1, 2, 1, 2, 1, 2, 15, 17, 2, 1, 2, 1, 2, 1, 2, 17, 20, 1, 2, 1, 2, 1, 2, 1, 2, 19
Offset: 1

Views

Author

Gary W. Adamson, Jul 27 2007

Keywords

Comments

Left column, congruent to {0, 1} mod 4, A042948: (1, 4, 5, 8, 9, 12, 13, 16, ...).
Row sums = A131912: (1, 7, 12, 18, 23, 29, 34, ...).

Examples

			First few rows of the triangle:
   1;
   4,  3;
   5,  2,  5;
   8,  1,  2,  7;
   9,  2,  1,  2,  9;
  12,  1,  2,  1,  2, 11;
  13,  2,  1,  2,  1,  2, 13;
  ...

Crossrefs

Cf. A131821, A128174, A042948, A131912.

Formula

2*A131821 - A128174 as infinite lower triangular matrices.
Previous Showing 21-30 of 59 results. Next

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